Problem 108 - Algebra and Trigonometry

Question

What is a reference angle? Give an example with your description.

Step-by-Step Solution

Answer

A reference angle is an acute angle formed by the terminal side of an angle in standard position and the x-axis. For instance, the reference angle for 120 degrees would be 60 degrees.

Step 1: Definition of Reference Angle

A reference angle is an acute angle, meaning it is less than 90 degrees, created between the terminal side of an angle in standard position and the x-axis.

Step 2: Process of obtaining a Reference Angle

To create a reference angle, first draw the angle in standard position. The angle is in standard position if it is placed on an (x, y) coordinate system with the vertex at the origin and the initial side on the positive x-axis. Then, identify where the terminal side intersects with the x-axis, if it were to be extended through the quadrant it is currently in. Draw a line between this point and the origin. The angle between this new line and the original terminal side is the reference angle.

Step 3: Example of a Reference Angle

For example, if given an angle of 120 degrees, it extends into the second quadrant. The reference angle is the acute angle between the terminal side of this angle and the x-axis. Here, the reference angle would be 180 degrees - 120 degrees, which equals to 60 degrees.